An Experimental Application of Total Energy Shaping Control: Stabilization of the Inverted Pendulum on a Cart in the Presence of Friction

Abstract—In this paper we report the experimental applica-tion of a state-feedback controller derived via the principles of Total Energy Shaping Control for the stabilization of underactuated mechanical systems. The particular application concerns the well-known inverted pendulum on a cart. We describe the first steps taken towards global stabilization of the inverted pendulum with Total Energy Shaping Control. The results show that performance of the nonlinear controller in the neighborhood of the equilibrium position is better compared to a linear H-infinity controller, since the transients are smoother and there is less overshoot. Furthermore, it is shown that the energy shaping controller has a great tuning potential that allows proper functioning of the closed-loop system in the presence of friction. This paper is intended to be the starting point in the development of tools that enable the control engineer to make deliberate choices in tuning the energy-shaping controller, based on performance in the presence of friction and in a later stage also for parameter uncertainties, input constraints and other issues that are relevant in a practical environment. Index Terms—Energy shaping, Hamiltonian systems, nonlin-ear control, passivity, underactuated mechanical systems with friction. I